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The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?

Travelling Salesman

Age 11 to 14 Challenge Level:

A Hamiltonian circuit (named after the Irish mathematician Sir
William Rowan Hamilton) is a continuous path in a graph that
passes
through each of the vertices exactly once and returns to
its
starting point.

How many Hamiltonian circuits can you find in these graphs?

Here is another classic problem. A salesman lives in
city A and he
has to visit the cities B, C and D. The distances
between the
cities are: AB = 120, AC=140, AD=180, BC=70, BD=100,
CD=110. Find
the shortest round trip from A through the other
three cities.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.